We introduce the notion of a “crystallographic sphere packing,” defined to be one whose
limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension …

Let (W, S) be an infinite Coxeter system. To each geometric representation of W is
associated a root system. While a root system lives in the positive side of the isotropic cone …

A theorem of Tits and Vinberg allows to build an action of a Coxeter group on a properly
convex open set of the real projective space, thanks to the data P of a polytope and re ection …

We explore visual representations of tilings corresponding to Schläfli symbols. In three
dimensions, we call these tilings 'honeycombs'. Schläfli symbols encode, in a very efficient …

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We investigate in this paper the relation between Apollonian d-ball packings and stacked
(d+ 1)(d+ 1)-polytopes for dimension d ≥ 3 d≥ 3. For d= 3 d= 3, the relation is fully …

The ball number of a link L, denoted by ball (L), is the minimum number of solid balls (not
necessarily of the same size) needed to realize a necklace representing L. In this paper, we …

In this paper we study various scribability problems for polytopes. We begin with the
classical k-scribability problem proposed by Steiner and generalized by Schulte, which asks …

Abstract A convex polytope PP in the real projective space with reflections in the facets of PP
is a Coxeter polytope if the reflections generate a subgroup Γ Γ of the group of projective …

We define Ford Spheres $\mathcal {P} $ in hyperbolic $ n $-space associated to Clifford-
Bianchi groups $ PSL_2 (O) $ for $ O $ orders in rational Clifford algebras associated to …